First Equation of Motion – Derivation he first equation of motion describes the relationship between the final velocity ( v v v ), initial velocity ( u u u ), acceleration ( a a a ), and time ( t t t ). It is expressed mathematically as: v = u + a t v = u + at v = u + a t This equation is fundamental in kinematics, particularly for objects moving with uniform acceleration. Let’s delve into its derivation step-by-step. Understanding Acceleration Acceleration is defined as the rate of change of velocity over time. Mathematically, this can be expressed as: a = v − u t a = \frac{v - u}{t} a = t v − u Here: a a a is the acceleration, v v v is the final velocity, u u u is the initial velocity, t t t is the time over which the acceleration occurs. Rearranging this equation allows us to express the final velocity in terms of the other variables: v − u = a t v - u = at v − u = a t By adding u u u to both sides, we arrive at: v = u + a t v = u + at v = u + a t This simple rearrange...
